Non-weight modules over the super Schrödinger algebra

Xinyue Wang; Liangyun Chen; Yao Ma

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 647-664
  • ISSN: 0011-4642

Abstract

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We construct a family of non-weight modules which are free U ( 𝔥 ) -modules of rank 2 over the N = 1 super Schrödinger algebra in ( 1 + 1 ) -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free U ( 𝔥 ) -modules of rank 2 over 𝔬𝔰𝔭 ( 1 | 2 ) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

How to cite

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Wang, Xinyue, Chen, Liangyun, and Ma, Yao. "Non-weight modules over the super Schrödinger algebra." Czechoslovak Mathematical Journal 74.3 (2024): 647-664. <http://eudml.org/doc/299307>.

@article{Wang2024,
abstract = {We construct a family of non-weight modules which are free $U(\mathfrak \{h\})$-modules of rank 2 over the $N=1$ super Schrödinger algebra in $(1+1)$-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free $U(\mathfrak \{h\})$-modules of rank 2 over $\mathfrak \{osp\}(1|2)$ are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.},
author = {Wang, Xinyue, Chen, Liangyun, Ma, Yao},
journal = {Czechoslovak Mathematical Journal},
keywords = {super Schrödinger algebra; simple module; U($\mathfrak \{h\}$)-free module; non-weight module},
language = {eng},
number = {3},
pages = {647-664},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-weight modules over the super Schrödinger algebra},
url = {http://eudml.org/doc/299307},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Wang, Xinyue
AU - Chen, Liangyun
AU - Ma, Yao
TI - Non-weight modules over the super Schrödinger algebra
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 647
EP - 664
AB - We construct a family of non-weight modules which are free $U(\mathfrak {h})$-modules of rank 2 over the $N=1$ super Schrödinger algebra in $(1+1)$-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free $U(\mathfrak {h})$-modules of rank 2 over $\mathfrak {osp}(1|2)$ are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.
LA - eng
KW - super Schrödinger algebra; simple module; U($\mathfrak {h}$)-free module; non-weight module
UR - http://eudml.org/doc/299307
ER -

References

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